I begin the thesis with an action research account of an intervention with respect to gender on a mathematics Post Graduate Certificate in Education (PGCE) course at a northern university in 1989-90. Two years after the intervention, I visited in their schools three of the students (now teachers) who had been involved and I interviewed each of them there, with a view to finding out what impact, if any, this intervention had had on their beliefs, understandings, commitments and practice. In the light of this experience, I sought out three teachers who had followed the course and who I had heard were working for change. I conducted several interviews with each of them. I constructed a model of the ways of knowing of (new) teachers of mathematics and linked one epistemology, that based on the authority of self and reason, to an emancipatory curriculum and to critical mathematics education. I have considered, briefly, the implications for initial teacher education. The research was conducted and this thesis is written as a praxis-orientated inquiry and both have been influenced by feminism, critical theory and postmodern tendencies. In this sense, the thesis itself is a research experiment.